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The sequence S is defined by Sn = 2(Sn – 1) – 4 for each int

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sandy
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The sequence S is defined by Sn = 2(Sn – 1) – 4 for each int [#permalink] New post   25 Jul 2018, 17:22
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The sequence S is defined by S_n = 2(S_{n – 1}) – 4 for each integer n ≥ 2. If S_1 = 6, what is the value of S_5?

(A) –20
(B) 16
(C) 20
(D) 24
(E) 36
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E
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sandy
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Re: The sequence S is defined by Sn = 2(Sn – 1) – 4 for each int [#permalink] New post   11 Aug 2018, 16:51
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Explanation

The sequence S_n = 2(S_{n - 1}) - 4 can be read as “to get any term in sequence S, double the previous term and subtract 4.”

The problem gives S_1 (the first term) and asks for S_5 (the fifth term):

6
S_1S_2S_3S_4S_5



To get any term, double the previous term and subtract 4. To get S_2, double S_1 (which is 6) and subtract 4: S_2 = 2(6) - 4 = 8.

Continue doubling each term and subtracting 4 to get the subsequent term:

68122036
S_1S_2S_3S_4S_5
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Re: The sequence S is defined by Sn = 2(Sn 1) 4 for each int [#permalink] New post   05 Jul 2023, 06:50
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The sequence S is defined by Sn = 2(Sn 1) 4 for each int [#permalink]
05 Jul 2023, 06:50
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